Our final recommended values from the RNCCSD method along with the previously calculated and experimental results for \(\alpha _d\) , \(\alpha _q\)  and \(B\)  are given in Table REF . The estimated uncertainties from our calculations are quoted beside the recommended values. These uncertainties account for the extrapolated contributions from the high-lying basis functions that are not included in the many-body methods, the neglected contributions from the higher-order Breit and QED interactions and from the neglected higher-level excitations. Errors due to the extrapolated basis functions and relativistic effects are analysed by employing the MBPT and RPA methods, while uncertainties due to the higher-level excitations are estimated by analysing contributions from the dominant triple excitations in the perturbative approach. Individual contributions from various sources to the above quantities are listed in Table REF  and the net uncertainty to the final value is given by adding all the contributions in quadrature. From these analyses, we recommend the values for \(\alpha _d\)  to be 38.99(31) a.u, for \(\alpha _q\)  to be 314(4) a.u and for \(B\)  to be \(-2195(50)\)  a.u.. We have also listed the previously reported experimental and calculated values of \(\alpha _d\) , \(\alpha _q\)  and \(B\)  in the above table. Results from the CC and RCC methods are given from both the CCSD method and the CCSD method with contributions from partial triple excitations (CCSD(T) method) along with their relativistic versions. The differences in the results from the CCSD and CCSD(T) methods can indicate importance of the neglected contributions from the triple excitations. The experimental value of \(\alpha _d\)  listed in Table REF  was measured by using Michelson twin interferometer technique [1]}. Later, this value has been revised by fitting the data using better numerical analyses [2]}. Our recommended value from the RNCCSD method agrees quite well with both the values. The latest calculation of \(\alpha _d\)  employs a sum-over-states approach, by combining only a few E1 matrix elements from the multiconfiguration Dirac-Fock (MCDF) method, experimental energies and the rest of the contributions are estimated using lower-order methods. This shows poor agreement with the experimental result [3]}. The calculations reported in Refs. [4]}, [5]} are equivalent to our RCCSD method, while calculations reported in Refs. [6]}, [7]}, [1]} are based on the FF approach using non-relativistic CC method. There seems to be an overall good agreement among all these calculations. It is worth mentioning that the recommended values given by the non-relativistic CC calculations of \(\alpha _d\)  in Refs. [6]}, [7]}, [1]} have used scaled values in order to quote more accurate values, but the actual calculations give very different values. Nonetheless, agreement of the previously reported accurate values of \(\alpha _d\)  for Zn with our RNCCSD result suggests that our estimated \(\alpha _q\)  and \(B\)  values using this method are reliable. There is one more calculation of \(\alpha _q\)  and \(B\)  reported using the non-relativistic CC method in the FF approach [1]}. As mentioned above, the final recommended values from these references are scaled values and the actual calculated values are again very different. For example, the CCSD results for \(\alpha _q\)  and \(B\)  are quoted in the above reference as \(360.16\)  a.u. and \(-2940\)  a.u. respectively. In the CCSD(T) method, the \(\alpha _q\)  value was modified to \(351.24\)  a.u. while the \(B\)  value was modified to \(-2780\)  a.u. [1]}. After scaling the result, the recommended values for \(\alpha _q\)  and \(B\)  were given as \(324.8(16.2)\)  a.u. and \(-2370(240)\)  a.u. respectively. Our RNCCSD results are obtained in the ab initio framework and they account for relativistic effects. It is, however, interesting to see that our results validate the recommended values that were reported in Ref. [1]}. It can be further noted that our RCCSD value for \(B\)  given in Table REF  differs substantially from the RNCCSD result. Therefore, good agreements of our RNCCSD results with the previously recommended values of \(\alpha _d\) , \(\alpha _q\)  and \(B\)  suggests that approximated RNCC method is more reliable compared to the approximated RCC method for the determination of the above quantities.
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